Ministers have backed a new law that will give effect to the Mother and Baby Institutions Payment Scheme.
The new bill was approved by Cabinet this morning and is expected to cost the state €800 million.
It's believed there may be around 34,000 former residents who will be eligible.
All mothers who spent time in such an institution will be entitled to a payment, with the amount increasing based on their length of stay.
Children who spent six months or more there will be entitled to a payment, depending on the time they spent in the homes.
Children's Minister Roderic O'Gorman is aiming to bring the bill before the Dail or Seanad, as soon as possible.